Question

ordering the angle measures of a triangle
the lengths of the sides of triangle abc are represented in terms of the variable m, where m>6.
ab = m - 2
bc = m + 4
ac = m
list the angles from smallest to largest.
angle angle angle

Explanation:

Step1: Compare the side lengths

Given \(AB = m - 2\), \(BC=m + 4\), \(AC = m\) and \(m>6\).
Subtract the expressions:
\(BC-AC=(m + 4)-m=4>0\), so \(BC>AC\).
\(AC - AB=m-(m - 2)=2>0\), so \(AC>AB\).
So the order of side lengths is \(AB

Step2: Use the triangle - angle relationship

In a triangle, the larger side is opposite the larger angle.
The angle opposite \(AB\) is \(\angle C\), the angle opposite \(AC\) is \(\angle B\), and the angle opposite \(BC\) is \(\angle A\).

Answer:

\(\angle C,\angle B,\angle A\)